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Sum Graphs and Geographic Information

Arlinghaus, Sandra Lach; Arlinghaus, William Charles; Harary, Frank; Arlinghaus, S. L.

Arlinghaus, Sandra Lach; Arlinghaus, William Charles; Harary, Frank; Arlinghaus, S. L.

1993-06-21

Citation:Arlinghaus, Sandra L.; Arlinghaus, William C.; Harary, Frank. "Sum Graphs and Geographic Information." Solstice: An Electronic Journal of Geography and Mathematics, Volume IV, Number 1. Ann Arbor: Institute of Mathematical Geography, 1993. Persistent URL (URI): http://hdl.handle.net/2027.42/60198

Abstract: We examine a new graph theoretic concept called a "sum graph," display a new sum graph construction, and prove a new theorem about sum graphs (sum graph unification theorem) verifying the construction. The sum graph is then generalized ultimately as an augmented reversed logarithmic sum graph so that it is useful in dealin with large sets of geographic information. The generalized form permits 1) the compression of large data sets, and 2) the simultaneous consideration of data sets at various levels of resolution.